{"paper":{"title":"Existence and multiplicity of solutions to a nonlocal elliptic PDE with variable exponent in a Nehari manifold using the Banach fixed point theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Amita Soni, D. Choudhuri","submitted_at":"2019-07-21T17:23:21Z","abstract_excerpt":"In this paper we study the existence and multiplicity of two distinct nontrivial weak solutions of the following equation in Nehari manifold. We have also proved that these solutions are in $L^{\\infty}(\\Omega)$. \\begin{align*} \\begin{split} -\\Delta_{p(x,y)}^{s(x,y)}u &= \\beta|u|^{\\alpha(x)-2}u+\\lambda f(x,u)\\,\\,\\mbox{in}\\,\\,\\Omega,\\\\ u &= 0\\,\\, \\mbox{in}\\,\\, \\mathbb{R}^{N}\\setminus\\Omega \\end{split} \\end{align*} Here, $\\lambda, \\beta > 0$ are parameters and $f(x,u)$ is a general nonlinear term satisfying certain conditions. The domain $\\Omega\\subset\\mathbb{R}^N (N\\geq 2)$ is smooth and bounded"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.09009","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}